Surface charge measurement

ABSTRACT

The invention relates to methods and apparatus for determining properties of a surface. Embodiments disclosed include an apparatus for measuring a surface charge of a sample, comprising: a sample holder having an opposed pair of electrodes and configured to hold a sample in position in a measurement volume between the electrodes such that a planar surface of the sample is aligned orthogonal to the electrode surfaces; a measurement chamber for containing a measurement liquid and having an open end configured to receive the sample holder to position the electrodes in a preset orientation; a laser light source positioned and configured to direct a laser beam through the measurement chamber between the electrodes and parallel to the planar surface of the sample when the sample holder is received in the measurement chamber; and a detector positioned and configured to detect scattered light from the measurement volume, wherein the apparatus is configured to allow for detection of the scattered light by the detector over a range of distances from the surface of the sample.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/126,673 filed on Dec. 16, 2013, which claims priority to PCTapplication number PCT/GB2012/051336, filed on Jun. 13, 2012, which, inturn, claims priority to U.S. provisional patent application No.61/497,385, filed Jun. 15, 2011. All of these applications are hereinincorporated by reference.

FIELD OF THE INVENTION

The invention relates to methods and apparatus for determiningproperties of a surface. Exemplary embodiments include methods andapparatus for determining a surface zeta potential by electro-osmoticflow measurement in a dip cell arrangement.

BACKGROUND OF THE INVENTION

The well known phenomenon of streaming potential is typically used tomeasure surface potential or charge of a material in an electrolyte.Measurements of capillary flow and on dispersions of finely dividedparticles may be used to determine surface charge. Measurementtechniques generally employ a specialist instrument dedicated solely tosuch measurements. Measurements using capillary flow or dispersedparticles may require that the sample material be in a particular formatthat may not always be convenient or straightforward to prepare.

U.S. Pat. No. 7,217,350 discloses a method of automatically determiningan electric charge-related characteristic or derived parameter ofparticles in a dispersion or of a cell wall, in which a dispersion isilluminated with light from a light source and light scattered byparticles in a detection volume is detected. In one arrangement thedetection volume comprises a transparent capillary cell with a pair ofelectrodes at opposing ends, forming a closed volume for a dispersion ofparticles in a liquid. In another arrangement a pair of electrodes isprovided on opposing side walls of a cuvette that is partly filled witha liquid sample.

U.S. Pat. No. 7,449,097 discloses an electrophoretic mobility measuringapparatus comprising a cell for confining a sample, the cell having atransparent electrode side wall and another electrode on an opposingcell wall. A voltage is applied across the electrodes and light isincident upon the inside of the cell through the transparent electrode.Scattered light is received through the transparent electrode and aDoppler displacement is measured.

US 2011/0210002 discloses a method and apparatus for measurement ofelectrophoretic mobility of particles and molecules in solution, inwhich a sample of particles is placed in a cell containing twoelectrodes across which is applied an alternating electric field. Amonochromatic light beam passes through the sample and light scatteredby particles is collected and collimated as it exits the cell. Opticalphase information is used to measure particle movement.

EP 2423671 discloses a particle characterization cell and instrument, inwhich a tubular cell main body forms an internal space with a pair ofelectrodes arranged to face each other in the internal space, laserlight irradiating a liquid sample in the internal space being scatteredby particles in the liquid sample and detected by a light detectingpart.

Each of the above mentioned documents disclose measurement ofelectrophoretic mobility of samples in the form of finely dividedparticles suspended in an electrolyte liquid.

SUMMARY OF THE INVENTION

Several aspects of the invention are presented in this application.Systems according to at least some of the aspects of the invention canbe advantageous in that they can provide a convenient, accurate, andreliable way to measure sample surface potentials.

In accordance with a first aspect there is provided an apparatus formeasuring a surface charge of a sample, comprising:

-   -   a sample holder having an opposed pair of electrodes and        configured to hold a sample in position in a measurement volume        between the electrodes such that a planar surface of the sample        is aligned orthogonally to the electrode surfaces;    -   a measurement chamber for containing a liquid electrolyte and        having an open end configured to receive the sample holder to        position the electrodes in a preset orientation;    -   a laser light source positioned and configured to direct a light        beam through the measurement chamber between the electrodes and        parallel to the planar surface of the sample when the sample        holder is received in the measurement chamber; and    -   a detector positioned and configured to detect scattered light        from the measurement volume,    -   wherein the apparatus is configured to allow for detection of        the scattered light by the detector over a range of distances        from the surface of the sample.

Detection of scattered light over a range of distances from the surfaceof the sample may be achieved by having a large illuminated area withmultiple detection points, having multiple illumination sources andmultiple detection points, and/or by allowing relative movement of thelight beam and sample holder. The first option may be achieved by thelight beam having a width extending over the range of distances, ormultiple light beams, and a detector, or multiple detectors, positionedfor measuring scattered light at multiple detection points at defineddistances from the sample surface. The second option, which may beprovided in addition to the first, may be achieved by allowing manual orautomatic movement of the sample in situ relative to the light beamand/or by moving the light beam relative to the sample surface.

An advantage of the apparatus according to the invention is that surfacecharge measurements can be taken of a material in a quicker and moreconvenient way compared to existing surface charge measurement systems,for example those using capillary cells. In particular, the relativeorientation of the sample surface to the electrodes, and the arrangementwhere the sample holder is insertable in, and removable from, ameasurement chamber, allows for a convenient measurement system foreasily prepared sample geometries.

The sample holder may comprise a first portion and a second portion,where the electrode pair is disposed at a distal end of the secondportion, the sample holder comprising an actuation mechanism fortranslating the second portion relative to the first portion. Anadvantage of the actuation mechanism is that the sample can bepositioned such that the sample surface is in a predefined positionrelative to the laser light beam, so that accurate and repeatablemeasurements can be taken as the sample is translated relative to thelight beam.

The actuation mechanism may be configured to translate the secondportion relative to the first portion in a direction parallel to theelectrode surfaces, or orthogonal to the surface of the sample.Maintaining an orthogonal arrangement between the light beam and theelectrodes, and between the electrodes and the sample surface, ensuresthat the light beam can be used to accurately measure the chargeproperties of the surface when immersed in the electrolyte.

The actuation mechanism may comprise a rotatable element such as acalibrated micrometric screw for linear translation of the secondportion relative to the first portion, an advantage of which is inrepeatable positioning over a range of positions of the sample relativeto the laser light beam. The actuation mechanism may be manuallyoperable, or may be electrically actuated.

The sample holder may be configured to be located in the measurementchamber in two or more distinct orientations such that the electrodesare located in two or more respectively different positions relative tothe measurement chamber. The sample holder may for example be configuredsuch that the electrodes are rotated 180 degrees between the first andsecond distinct orientations. An advantage is that the two or moreconfigurations can be used to position the sample in preset positionsrelative to the laser light beam for simple and quick measurements onthe sample without the need for fine adjustment of the sample holder.The number of distinct configurations is preferably only two, althoughfurther configurations are possible. The sample holder and measurementchamber may comprise correspondingly shaped stepped mating surfaces toachieve the two or more configurations when the stepped mating surfacesare engaged with each other.

The apparatus may further comprise a calibration jig configured to holdthe sample holder in a predefined position such that the sample surfacein position between the electrodes can be translated to a predeterminedlocation relative to the first portion of the sample holder, and therebyrelative to the laser beam when the sample holder is positioned in themeasurement chamber. An advantage of using a calibration jig is that thesample can be accurately positioned without the need to determine thedistance between the laser light beam and the sample surface when thesample holder is positioned in the measurement chamber.

The apparatus is preferably configured to determine a measure ofmovement of tracer particles suspended in the electrolyte in themeasurement volume between the electrodes from scattered light detectedby the detector. The measurement of particle movement may be determinedby Doppler analysis of the scattered light. The apparatus may be furtherconfigured to determine a measure of surface potential of the sample byextrapolation of two or more measurements of movement of tracerparticles at different relative distances between the laser light beamand the sample surface.

The apparatus is preferably configured to apply an alternating voltageto the opposed pair of electrodes to provide an alternating electricfield between the electrodes across the planar surface of the sampleduring detection of the scattered light by the detector. The alternatingvoltage may be in the form of a square wave comprising half cycles withan optional interval between each half cycle where no voltage isapplied. Each half cycle, i.e. the portion of the alternating voltagewhere either a positive or a negative voltage is applied across theelectrodes, may be of 75 ms or longer in duration, optionally between 75ms and 1200 ms, and further optionally around or below 300 ms. Theoptional interval between each half cycle may be between 0 and 1000 ms,with a particular preferred interval of around 200 ms.

In accordance with a second aspect there is provided a method ofmeasuring surface charge of a sample, comprising:

-   -   providing a sample holder having an opposed pair of electrodes        with a sample held in position in a measurement volume between        the electrodes such that a planar surface of the sample is        aligned orthogonal to the electrode surfaces;    -   receiving the sample holder in an open end of a measurement        chamber containing a liquid electrolyte to position the        electrodes in a preset orientation;    -   directing a light beam from a laser light source through the        measurement chamber between the electrodes and parallel to the        planar surface of the sample with the sample holder received in        the measurement chamber; and    -   detecting scattered light from tracer particles suspended in the        liquid electrolyte in the measurement volume with a detector    -   wherein scattered light is detected by the detector over a range        of distances between the laser beam and the planar surface of        the sample.

Optional and preferable features of the second aspect of the inventionmay correspond with those of the first aspect, as described above.

In accordance with a further aspect of the invention there is provided azeta potential measurement apparatus for measuring a zeta potential of asurface of a sample using tracer particles, comprising:

-   -   a first electrode surface,    -   a second electrode surface separated from the first electrode        surface along a first axis,    -   a vessel defining a measurement volume between the first and        second electrodes, and    -   a holder for holding the sample adjacent the measurement volume        at a position between the first and second electrodes, and    -   an optical detector responsive to one or more locations within        the measurement volume and operative to detect motion of the        tracer particles at the plurality of different locations within        the measurement volume.

The apparatus may further include a motive mechanism provided betweenthe sample and the detector to induce relative motion between the sampleand detector to cause the detector to be responsive to a plurality ofthe locations. The motive mechanism may be manually actuated. The motivemechanism may be joggle-based, i.e. based on the sample holder beinglocatable in the measurement chamber or vessel in two or more distinctorientations. The motive mechanism may be electrically actuated. Thedetector may be an autocorellating PALS detector.

The apparatus may further include a processor operative to calculate thezeta potential based on differences in reported potential anddisplacement at the plurality of different locations.

The electrode surfaces may be parallel and the plurality of locationsmay be positioned along a second axis perpendicular to first axis.

The first and second electrodes, the vessels, and the holder may all beheld in a removable cuvette that is constructed to sit in an instrumentthat includes the detector.

In accordance with a further aspect of the invention there is provided amethod of obtaining zeta potential measurements for a surface of asample using tracer particles, comprising:

-   -   contacting the sample with an electrolyte,    -   introducing tracer particles in the electrolyte,    -   applying an electric field across the electrolyte, and    -   measuring displacement of the tracer particles at one or more        positions within the electrolyte.

The method may further include the step of deriving the zeta potentialfrom results of the step of measuring.

The method may be applied to a sample that includes a plastic material.The method may be applied to a sample that includes a solid biologicalmaterial.

The step of measuring displacement may include measuring a displacementat at least two positions, optionally at least three positions, withinthe electrolyte.

In accordance with a further aspect of the invention there is provided amethod of obtaining zeta potential measurements for a surface of asample using tracer particles, comprising:

-   -   means for contacting the sample with an electrolyte with        suspended tracer particles,    -   means for applying an electric field across the electrolyte, and    -   means for measuring displacement of the tracer particles at one        or more positions within the electrolyte.

The means for contacting may include a dip cell that includes means forholding the electrolyte with suspended tracer particles and means forholding the sample at a predetermined position in the means for holding.

DETAILED DESCRIPTION

Aspects and embodiments of the invention are described in further detailbelow by way of example and with reference to the enclosed drawings inwhich:

FIG. 1 is a perspective schematic diagram of an illustrative zetapotential measurement instrument according to the invention;

FIG. 2 is a schematic diagram illustrating flow geometry for a surfaceunder test;

FIG. 3 is an elevation view diagram of a sample holder test cell for theinstrument of FIG. 2;

FIG. 4 is a cross-sectional diagram of a sample holder test cell headfor the instrument of FIG. 2 showing different measurement beampositions for different test cell head positions;

FIG. 5 is a perspective drawing of an implementation of the sampleholder test cell of FIG. 3;

FIG. 6 is a plan view diagram of the sample holder test cell of FIG. 3in position in an adjustment or calibration jig;

FIG. 7 shows side elevation views of an exemplary sample holder testcell configured for two distinct orientations relative to a measurementchamber;

FIG. 8A is a plot of voltage applied to the test cell of FIG. 3 as afunction of time;

FIG. 8B is a plot of voltage applied to the test cell along with currentpassing through the test cell as a function of time;

FIG. 9 is a schematic diagram of the test cell electrode assembly ofFIG. 4 illustrating particle and fluid flow resulting from voltageapplied to the cell at different measurement positions;

FIG. 10A is a family of plots of displacement (as indicated by phase) asa function of time for the measurement positions A to E illustrated inFIG. 9;

FIG. 10B is a further family of plots of displacement as a function oftime for an increased number of measurement positions;

FIG. 11 is a plot of reported potential as a function of displacementfrom the sample surface for the measurement positions illustrated inFIG. 9;

FIG. 12 is a plot of R² as a function of displacement for water atvarious temperatures;

FIG. 13 is a plot of surface potential for a series of measurements fora PTFE sample;

FIG. 14 is a plot of surface charge as a function of pH for a PTFEsample measured using the instrument of FIG. 1 and with othertechniques;

FIG. 15 is a plot of surface potential as a function of pH for a sampleof silica measured using the instrument of FIG. 1 and with othertechniques;

FIG. 16 is a plot of surface potential normalized to a value recorded at25° C. as a function of temperature for the instrument of FIG. 1 andwith other techniques;

FIG. 17 is a plot of surface potential as a function of pC for a PTFEsample measured using the instrument of FIG. 1 and using othertechniques;

FIG. 18 is a plot of surface potential as a function of pC for apolycarbonate sample measured using the instrument of FIG. 1 and usingother techniques;

FIG. 19A is a plot of apparent zeta potential as a function ofdisplacement for a sample of clean PTFE in Goethite at pH 3.5;

FIG. 19B is a plot of apparent zeta potential as a function ofdisplacement for a sample of PTFE with dried-on Goethite in Goethite atpH 3.5;

FIG. 19C is a plot of apparent zeta potential as a function ofdisplacement for a sample of PEEK 450G in DTS0230 at pH 9.0;

FIG. 19D is a plot of apparent zeta potential as a function ofdisplacement for a sample of PTFE in DTS0230 at pH 9.0;

FIGS. 20A to 20E are plots of normalised particle displacementmeasurements over time intervals varying between 75 ms (FIG. 20A) and600 ms (FIG. 20E) as a function of displacement from the surface of asmooth flat PTFE block in 1 mM KCl at pH 9.0 and pH 2.67.

Referring to FIG. 1, an exemplary surface charge measurement instrument10 according to an aspect of the invention includes a light source 14, asample cell 16 for holding a sample 22 under test with its test surface12 in contact with an electrolyte, and a detector 18. The instrument 10may be used to determine the zeta potential of the test surface 12 ofthe sample 22 under test. Although other configurations are possible,the light source 14 and the detector 18 preferably form part of aparticle measurement system along with other optical elements thatenable the system to perform a laser Doppler phase electrophoreticanalysis light scattering measurement protocol, such as is described inreference [12]. Particle measurement instruments of this type areavailable from Malvern instruments Ltd of Malvern, UK, examples of whichare described further in international patent applicationPCT/GB2009/051350, published as WO/2010/041082 and as U.S. Pat. No.9,341,564, issued May 17, 2016, which is herein incorporated byreference.

Referring also to FIG. 2, the instrument 10 operates according to anoptical technique that measures the electro-osmotic flow of anelectrolyte near a single charged test surface 12 with an external fieldapplied parallel to the surface. The technique uses a single test platepresented to the optical detection system in a convenient ‘dip cell’format that can fit inside a standard type of cuvette and can thereforebe used in instrumentation intended for electrophoresis measurements,such as the Zetasizer range of instruments from Malvern Instruments Ltd.

A surface 12 under test is immersed in an electrolyte 96 with anexternal electric field E_(x) applied. The technique is characterized bydisplacements of the order of 100's of micrometres (μm) and the slippingplane of the surface 12 under test can then be assumed to coincide withthe plane of y=0. The electric field E_(x) and the presence of the ionicspecies within the electrolyte cause electro-osmotic fluid motion alongthe surface at y=0.

Assuming that the system has no pressure gradients, is slow flowing andin a steady state, the Navier-Stokes equation reduces to

$\begin{matrix}{{\rho \; \overset{.}{v}} = {\eta \left\lbrack {\frac{d^{2}v}{{dx}^{2}} + \frac{d^{2}v}{{dy}^{2}}} \right\rbrack}} & (1)\end{matrix}$

where v(t,x, y) is the component of fluid velocity parallel to theboundary, ρ is the fluid density and η is the fluid viscosity. Theco-ordinate x is parallel to the boundary, and y is perpendicular.Because there is no flow perpendicular to the boundary, continuityimplies that v is not a function of x, and the equation simplifies tothe following one dimensional homogenous heat or diffusion equation:

$\begin{matrix}{\overset{.}{v} = {k\left\lbrack \frac{d^{2}v}{{dy}^{2}} \right\rbrack}} & (2)\end{matrix}$

where k=η/ρ. This, with the initial condition that v(0,y)=0 and boundarycondition v(t,0)=v_(eo) where v_(eo) is the fluid velocity at theboundary we have a problem on the half line (0, ∞) with homogenousinitial conditions and Dirichlet boundary conditions and has a Greenfunction solution that can be expressed in closed form as follows:

$\begin{matrix}{{v\left( {y,t} \right)} = {\int_{0}^{\infty}{\frac{1}{\sqrt{4\pi \; {k\left( {t - s} \right)}^{3}}}\exp \frac{y^{2}}{4{k\left( {t - s} \right)}}v_{eo}{ds}}}} & (3)\end{matrix}$

This has the following closed form solution:

$\begin{matrix}{{v\left( {y,t} \right)} = {v_{eo}\left\lbrack {1 - {{erf}\left( \frac{y}{2\sqrt{kt}} \right)}} \right\rbrack}} & (4)\end{matrix}$

where erf is the error function. For water at 25° C. the term in squarebrackets in equation (4) disappears at y≧750 μm for t≧75 ms or y≧1.5 mmfor t≧300 ms. Time intervals of this magnitude are typical formonitoring electrophoretic motion using PALS and adjustment of thesurface under test with respect to the detection optics is easilyachieved within these distances with a micrometer stage. Therefore, afit of equation (4) to measurements of v_(i)(y_(i)) at various pointsy_(i) can then be extrapolated to the y-axis intercept to yield v_(eo).This is described in more detail in section 2.2.2.1 of reference [35].The relationship between the surface zeta potential ζ and v_(eo) isgiven by:

$\begin{matrix}{\frac{v_{eo}}{E_{x}} = \frac{ɛ\zeta}{\eta}} & (5)\end{matrix}$

where E_(x) is the electric field strength, ε the electrolyte relativepermittivity and η the electrolyte viscosity (see also reference [11]).

The fluid motion measurement (at points y_(i)) is achieved by detectionof the movement of tracer particles dispersed in the electrolytealongside the surface under test, with the mobility being measured usinga PALS (Phase Analysis Light Scattering) technique.

Referring also to FIGS. 3 to 5, the sample holder test cell 16 includesa first portion 34 and a second portion in the form moveable section 36having a test cell head 20 supported by, and located at a distal end.The test cell head 20, further detailed in FIG. 4, includes a pair ofelectrodes 24, 26, which are preferably plate-shaped, i.e. planar. Theelectrodes 24, 26 are positioned either side of a measurement volume 27in which a test sample 22 can be located with a planar test surface 12oriented orthogonally to the planar surfaces of the electrodes 24, 26.In use, the test cell head 20 comprising the electrodes 24, 26 and testsample 22 is immersed in an electrolyte that includes tracer particles,the electrolyte providing a medium across which an electric field isapplied by the electrodes 24, 26.

The sample holder 30 includes an adjustment mechanism 32, such as amicrometer, which is supported by a static section 34. The adjustmentmechanism 32 allows the position of the test cell head 20 to be adjustedrelative to the static section 34 in a direction normal to the testsurface 12 so that a measurement beam 28 (FIG. 4) from the light source14 is directed across the test surface 12 over a range of distances fromthe test surface 12. The supporting section 32 of the test cell body 30may include one or more interface surfaces 38 that interfacemechanically and electrically with portions of the instrument to allowthe test cell to be removably and precisely positioned in the instrumentwith respect to the measurement beam 28. In the exemplary embodimentillustrated in FIG. 5, the test cell 16 is designed to conform to astandard form factor for test cuvettes for the above mentioned Zetasizerinstrument line. The adjustment mechanism 32 may be manually operated ormay be motorized.

The test cell 16 may be mounted in a calibration jig 40, as shown inFIG. 6. The adjustment mechanism 32 can then be used to adjust theposition of the surface of the test sample 22 until there is no gapbetween the surface and a corresponding mating surface of thecalibration jig 40 (indicated at position A in FIG. 6). A user can thenset the adjustment mechanism 32, for example in the form of amicrometer, to a required measurement position from this datum. Thistechnique allows for different test plate thicknesses to beaccommodated. The test cell 16 can then be removed from the jig andimmersed in the measurement chamber, or cuvette, containing tracerparticles dispersed in the target liquid electrolyte, and placed in theinstrument for measurement.

In general, the data obtained using the test cell of the type describedherein tend to be highly reproducible, with standard engineeringtolerances being sufficient to reduce uncertainties to a minimum. Forincreased reproducibility, an additional feature may be incorporated inthe test cell, an example of which is illustrated in FIG. 7. In thisembodiment, a micrometer adjustment mechanism is used to set the correctheight of the test surface with respect to the beam to accommodate thethickness of the test sample, for example using a calibration jig asdescribed above. Once calibrated, the test cell may be positioned in twoor more preset measurement positions relative to the measurementchamber, each position having a preset distance between the measurementbeam and the test surface of the sample. This may be achieved byproviding a stepped region 38 on the static or supporting section 34 ofthe test cell, the stepped region 38 allowing for two differentpositions depending on the orientation of the test cell relative to themeasurement chamber. In the exemplary embodiment illustrated in FIG. 7,the test cell may be rotated through 180° (π radians) to select whichrelative position is chosen. If the linear assumption according to therelationship in equation 2 is correct, two measurement positions shouldbe sufficient to obtain a value for both m and v_(eo). For increasedaccuracy, however, further preset positions may be preferred, which maybe achieved for example by providing a series of two or more steppedregions allowing for a corresponding plurality of different measurementpositions.

In one exemplary embodiment, the test cell may have a 500 μm pitchthread and the cell position y, i.e. the distance between the staticsection 34 and the end of the moveable portion 36, may be adjusted bywinding an adjustment knob against a biasing force provided by a spring,thereby reducing hysteresis and relative positional uncertainty to lowor negligible levels. In order to set a zero point for a plate ofarbitrary thickness, the cell can be adjusted downwards relative to themeasurement chamber until the laser beam is on the point of beingobscured, as determined by monitoring a count rate in the forward angle.In this exemplary embodiment, the laser beam passes through the cell asshown in FIG. 1 with a beam width or around 40 μm, resulting in amaximum uncertainty of around ±20 μm. Particle mobility data may also berecorded and the results can be reduced using the relationship ofequation 4.

In operation, referring also to FIG. 9, charged tracer particles 95suspended in the liquid electrolyte 96 move under the application of theelectric field between the opposing electrodes 24, 26. The tracerparticles 95 scatter light from the illuminating beam, which is detectedby the detector 18. By use of a reference beam 29 (FIG. 1) split offfrom the incident beam 15 prior to illuminating the sample, the phase ofthe scattered light 17 relative to the incident light 15 can bemeasured. This phase is linearly related to the speed of the tracerparticles 95 in the measurement liquid 96. Since the static orsupporting section 34 of the test cell 30 is fixed relative to theilluminating optical measurement beam 28 (FIG. 4), the plate positioncan be altered by means of the adjustment mechanism 32 (FIG. 5), such asa micrometer, thereby translating the moveable section 36 (FIG. 3)relative to the supporting section 34 and therefore with respect to themeasurement beam 28. Multiple measurements can thereby be taken for asample with the measurement beam 28 at multiple distances from the testsample surface 12.

As illustrated schematically in FIG. 9, on the application of anelectric field across the measurement volume between the electrodes 24,26, the tracer particles 95 move under the influence of both theelectro-osmotic motion of the fluid, v_(i)(y_(i)) (indicated by solidvectors 91A-D) and due to electrophoretic motion, v_(ep) (indicated bydashed vectors 92A-E). The total detected motion is given by the sum ofthese vectors, which in FIG. 9 is indicated by dotted vectors 93A-E. Thefield strength, E_(x), can be determined from a measurement of theconductivity of the measurement liquid and a measurement of electriccurrent during application of the field. This tends to yield a moreaccurate estimate of E_(x) than by calculating the field from thepotential applied to the cell.

FIG. 8A illustrates a plot of voltage applied to the electrodes of anexemplary test cell over time. In this case, the voltage is switched ata frequency of around 0.42 Hz, which is done to minimize anypolarization concentration effects due to charge migration, which cancause increased uncertainty in the current estimate during the fieldapplication. An off-time 50 of around 200 ms between successiveapplications of opposing voltages over 600 ms periods is used in orderto allow the system to relax to zero before a subsequent reversepolarity is started.

FIG. 8B is a further plot of voltage 81 (left hand scale) and current 82(right hand scale) as a function of time for an exemplary test cell. Thevoltage 81 is applied in the form of a series of square wave pulses, andthe resulting current 82 peaks after the rising and falling edges ofeach pulse, followed by a gradual decay.

FIG. 10A illustrates a series of plots of phase (corresponding toparticle displacement) as a function of time. The displacement per unittime (i.e. particle velocity) falls to around zero during the intervalbetween successive voltage pulses. The overall displacement during eachon-time pulse is taken as the average over the whole of the on-timeperiod. This is based on a simplified model that ignores effects such asthose due to inertia or pressure gradients but, as the results in thefollowing sections show, this simple model provides measurements thatare reasonably linear, in accordance with the relationship in equation2, and which yield results that are precise and accurate in comparisonto literature values based on other techniques. FIG. 10B illustrates asimilar series of plots of phase as a function of time, for an increasednumber of beam positions relative to the sample surface.

Different measurement strategies can be employed to obtain a measure ofsurface charge of a sample. A set of measurements may be taken using aslowly varying field, as described above, at multiple beam positions,the positions set using adjustment of a micrometer. The micrometer maybe motorised or manually adjusted. Slowly reversing field measurementsmay alternatively be taken at two positions only, for example byreversing the orientation of a suitably configured sample holder, asillustrated in FIG. 7 and described above. This may lead to increaseduncertainty due to an extrapolation based only on two data points, buthas an advantage of simplifying operation and improving repeatability.

Alternative types of measurements can be performed where one or twopositions are used for the measurement. An appropriate model is fittedto the slow field phase plot and the electro-osmosis and electrophoresiscalculated from the model. The electrophoresis may be measured either atthe same position as the slow field or at the second positions, furtheraway from the wall. This measurement strategy allows the determinationof the sign of the wall charge, and is discussed in more detail in U.S.Pat. No. 7,217,350 and EP 1154266, which are both herein incorporated byreference.

The reported zeta potential values from measurements taken on a sampleconsisting of a PTFE block immersed in a pH 9.2 buffer and usingCarboxylated latex tracer particles are shown in FIG. 11, as plottedagainst the displacement from the surface. As the optical detectionposition moves away from the surface (points A to D), theelectro-osmotic contribution to the resulting motion reduces in valueuntil, at some position E, the detected motion is in effect only theelectrophoretic motion of the tracer from which the tracer zetapotential ζ_(ep) can be calculated (corresponding to the region betweenpositions D and E in FIG. 11). The y-axis intercept can be extrapolatedfrom a linear fit to the data over points A to D and the surface zetapotential at the slipping plane, i.e. where y=0, is then given by thefollowing:

ζ_(wall)=−Intercept+ζ_(ep)   (6)

The data were reduced using a least squares linear regression of thepotentials reported at each displacement against the displacement fromthe surface. The standard error in the intercept was then added inquadrature to the uncertainty in the electrophoretic mobility (recordedat position E) in order to give a measure of overall uncertainty in thesurface zeta potential. A linear fit avoids the region beyond point Dwhilst, conversely, extending as far out as possible from the surface,in order to provide a more accurate estimate of the slope and therebythe intercept.

The viscosity of the dispersant in which the cell is immersed willchange with temperature. Specifically, less viscous fluids will coupleless efficiently with increasing distance from the sample surface andtherefore we would expect higher temperatures to exhibit a lowerelectro-osmotic component at the same distance than at lowertemperatures. To assess this, a silica plate was measured in 1 mM KCl atpH7.0 +/−0.1 using a milk substitute as the tracer. The results arepresented in the form of R² values of the mean values of reportedpotential at displacements of up to y=750 μm and for a range oftemperatures, as plotted in FIG. 12. At 25° C. the fit is good(indicated by an R² value close to 1) out to greater than 750 μm but, asexpected, as the temperature increases the linear region reduces inextent with even a 5° C. increase in temperature enough to reduce the R²value from >0.99 to approximately 0.97 at 750 μm. As a result,measurements are preferably conducted at or around ambient temperature,nominally 25° C., and with a maximum displacement set by the point atwhich the R² value falls below 0.99.

Various measurements were performed to demonstrate the accuracy,precision and reproducibility of the new technique using a comparisonwith measurements by other techniques reported in the literature.Reproducibility of the technique was investigated for a known wellbehaved system of a PTFE block and 300 nm carboxylated latex beadsdispersed in pH9.2 buffer. Latex is known to have a stable zetapotential of −68 mV +/−10% at this pH, which can be measured using LaserDoppler Electrophoresis (LDE) for extended periods without degradation.Measured surface potentials of the PTFE sample are shown in FIG. 13.Each experiment was conducted with a new tracer dispersion and afterhaving cleaned the PTFE block and electrodes with Helmanex® followed bycopious amounts of deionised water and a brush.

TABLE 1 Literature values for PTFE surface potential in a 1 mM saltsolution at pH 9. Surface Potential/mV Reference Capillaryelectrophoresis −57 [6] Streaming potential −78 [1] Capillaryelectrophoresis −65 [7]

No outliers were removed from the data in FIG. 13 and the overallsurface zeta potential result of −70.0 mV+/−7.5 mV is in excellentagreement with the mean value from the available literature valuesindicated in Table 1 above of −67.0 mV+/−11 mV. The Goethite, NISTtraceable standard for dispersed zeta potential measurements quotes apass/fail RSD of 10%, indicating that the technique is capable ofreproducing surface potential measurements to approximately the sameuncertainty, given by −(7.5/70)×100%=11%.

Titrations of surface potential against pH are likely to be one of theprimary applications for this technique. A series of measurements ofPTFE and silica were conducted in 1 mM KCl and the pH varied using HCland KOH. A milk substitute (described in further detail in reference[35]) was used as a tracer for all measurements. Each pH pointcorresponds to a separate measurement sequence using the cell.

FIGS. 14 and 15 show that the results are in good general agreement withstreaming potential, dispersed particles and capillary electro-osmosismeasurements at all pH values tested in the region of the isoelectricpoint (IEP). There is less general agreement at higher pH values butthis appears to be a general feature of all techniques. For dataobtained by the new technique, the surface potential would be expectedto saturate at high (and low) pH as all available surface charge groupsare ionised. Looking at the error bars in both plots, no trend betweenthe uncertainty and pH is seen to exist, with a typical uncertainty of+/−2 to 3 mV. The isoelectric point for the milk substitute is at pH4.No increase in uncertainty in the reported surface potential is detectedeither when the surface IEP is at approximately the same value as thesurface (FIG. 14) or at a different value (FIG. 15). This indicates thatthe IEP of the tracer may be ignored as long as the experiment does notextend for long enough for it to stick to the surface under test. Inthis case, each displacement took 120 s to record, but a singledispersion was used for each pH point over five or six displacementpositions so the samples were immersed for up to 20 minutes without anyapparent reduction in accuracy.

Kirby & Hasselbrink (reference [22]) note that the scientific record issparsely populated with studies concerned with the relationship betweensurface potential and temperature. A small number of notablecontributions exist which strongly disagree with each other. As acomparison, the surface potential of a Silica test plate was measured asan application specific demonstration of the performance of thetechnique with temperature. Much of the experimental evidence for therelationship between zeta potential and temperature is due to Ishido &Mizutani (reference [2]) and Somasundaran & Kulkani (reference [26]),whose streaming potential measurements predict an increase of 1.75% per° C. in zeta potential of silica in 1 mM and 10 mM KNO₃ at pH7.0. Anuncoated microscope slide was cut and mounted in the cell and thesurface zeta potential measured in 1 mM KCl at pH 7.0 +/−0.1. The dataare shown in FIG. 16 with a plot of surface potential, normalized to thevalue recorded at 25° C., against temperature. Our data predict a slopeof 0.34%, which is in poor agreement with the streaming potentialresults but is in excellent agreement with a more recent study usingcapillary electrophoresis by Evenhuis et al (reference [5]), whomeasured a slope of 0.39% per ° C. The error bars demonstrate that thetechnique is reproducible with temperature variation with an RSD varyingfrom 5% to 10% and that no apparent increase in uncertainty exists withtemperature. The whole cell (dip cell, cuvette and dispersant) isimmersed in the instrument's temperature controlled cell block andsetting each temperature is therefore simpler to implement in comparisonto other techniques as the whole apparatus can be kept at the same settemperature (See reference [22]).

Increasing salt concentration increases the current passed for the samefield strength, which can cause Joule heating and polarizationconcentration effects. These can increase the uncertainty in therecorded particle mobility. Surface potential measurements ofPolycarbonate and PTFE test blocks in KCl were carried out between 0.1mM and 50 mM salt concentration with a milk substitute used as thetracer. In order to avoid Joule heating the conductivity of the samplewas measured before and after the electrophoresis measurement and thefield strength titrated down until the difference in conductivity andtherefore sample temperature was negligible. Table 2 below shows thefield strengths and subsequent integration times used to maximize thesignal to noise at each concentration C, where, pC=−log C.

TABLE 2 Field strength and integration times against pC. Integrationtime per pC Field Strength, V/cm displacement point. s 1.5 6.25 25 212.5 20 3 25 13 4 25 13

The data for PTFE are shown in FIG. 17 and for polycarbonate in FIG. 18.Firstly, we note that with the field strengths and integration timesused in Table 2, no relationship between the uncertainty in themeasurements and pC is apparent. The uncertainties in the PTFE data areof the order of the spread in the mean results from all techniques andsignificantly less so for the polycarbonate case.

We would expect a linear relationship between surface potential and pCpassing through the origin between surface potential and saltconcentration for monovalent counter ions. The polycarbonate dip celldata are self consistent in that they fit linearly with near zerointercept but there is considerable variation amongst the references.Since both the dip cell and the Roberts et al data (reference [23]) arelinear with low intercept then we can attribute the difference to agenuine difference in sample properties such as surface smoothness, forinstance—in our case, the polycarbonate was a small block removed from amoulded part with a highly polished surface. The PTFE results are ingood overall agreement with the literature values although an overallintercept of zero is less convincing in these data, with a more likelyintercept nearer to +20 mV.

FIGS. 19A to 19D illustrate further results of reported zeta potentialfor various combinations of samples and electrolytes. FIG. 19A indicatesresults from a clean PTFE plate in a Goethite solution at pH 3.5. FIG.19B indicates results from a PTFE plate having dried-on Goethite in aGoethite solution at pH 3.5. The differences between these sets ofmeasurements indicate the importance of ensuring a clean sample toobtain accurate measurements of the sample material uncontaminated bysuspended or dissolved material in the electrolyte. FIG. 19C indicatesresults from a PEEK 450G plate in a DTS023 solution at pH 9.0, and FIG.19D indicates results from a PTFE plate in the same type of solution.The results from these measurements are summarised below in Table 3,with selected results compared with those from reference [1].

TABLE 3 Summary of results from FIGS. 19A-D, in comparison withliterature values (*streaming potentials from reference [1]). MeasuredStreaming Test surface Tracker particle pH wall charge potential result*PTFE Carboxylated 9.0 −70 mV −80 mV pH latex 9.0 KCl PEEK 450GCarboxylated 9.0 −45 mV latex PTFE with dried Goethite 3.5  10 mV onGoethite PTFE Geothite 3.5 −1.5 mV  2.5 mV pH 3.5 KCl

FIGS. 20A to 20E illustrate plots of normalised particle displacementmeasurements for time intervals between 0 and 75 ms (FIG. 20A), 0 and150 ms (FIG. 20B), 0 and 300 ms (FIG. 20C), 0 and 450 ms (FIG. 20D) and0 and 600 ms (FIG. 20E) for a smooth, flat PTFE block mounted andmeasured in 1 mM KCl at pH 9.0 and pH 2.67. At pH 9.0 the surface ishighly negatively charged and at pH 2.67, highly positively charged (seereference [1]). The milk substitute used for the tracer particles wasalso negative at pH 9.0 and positive at pH 2.67 (see further details inAppendix B of reference [35]). Each field half cycle was 600 ms in totalduration. A least square linear fit was applied to the phase plot (FIG.10A) over various subsets of 75 ms, 150 ms, 300 ms, 450 ms and 600 ms ofthis interval to yield an average phase shift per unit time at eachdisplacement point A-E. The total particle displacement in the timeinterval in question, at each distance from the test surface, isdirectly proportional to the average total phase shift during the ontimepulse (FIG. 8A). This total particle displacement is plotted in each ofFIGS. 20A to 20E. The experimental data were also normalised between a2nd order polynomial extrapolation of the data to the intercept (y=0)and from an estimate of the asymptote towards point E indicated in FIG.9. This asymptote is due to the limiting electrophoretic mobility of thetracer particles in the absence of any electro-osmotic flow far from thesurface. Normalisation removes the tracer velocity and allows directcomparison of the data with the model indicated by equation (4) above.The fit to the model is excellent for the phase data at and below 300 msfor both positively and negatively charged surfaces. Above 300 ms thefit is less convincing and we attribute this to a gradual build up inback pressure which works to suppress the electro-osmotic flow. Furtherexplanation of these results, and the associated model, is disclosed inreference [35], the contents of which are incorporated by referenceherein.

In conclusion, a new, simpler technique for the measurement of surfacezeta potential using laser Doppler electrophoresis has been presented.The technique is shown to be characterized by a relative standarddeviation in reproducibility of less than or equal to around 10% forwell behaved systems, yielding accurate and reproducible surfacepotential values in excellent agreement with literature values fromstreaming potential, electro-osmotic (capillary) flow and particledispersions for various surface types, temperatures up to 40° C. andionic strengths in the range 0.1 mM to 50 mM.

In the embodiment described, control and measurement functions can beperformed by a computer workstation running a standard operating system,such as Microsoft Windows® or Linux®, and special-purpose software. Theworkstation can allow the user to perform individual measurements, andit can also use sequencing functionality to fully automate electricaland mechanical operations. It is also possible to create animplementation that is based on specialized custom hardware, or acombination of the two approaches.

The present invention has now been described in connection with a numberof specific embodiments thereof. However, numerous modifications whichare contemplated as falling within the scope of the present inventionshould now be apparent to those skilled in the art. For example, whilemicrometer- and joggle-based approaches have been shown to adjust thedetection position, other approaches such as moving mirrors could alsobe employed. Therefore, it is intended that the scope of the presentinvention be limited only by the scope of the claims appended hereto. Inaddition, the order of presentation of the claims should not beconstrued to limit the scope of any particular term in the claims. Alldocuments referenced in this application are herein incorporated byreference for all purposes.

REFERENCES

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What is claimed is:
 1. A zeta potential measurement apparatus,comprising: a measurement chamber; a laser light source positioned andconfigured to direct a laser beam through the measurement chamber; adetector positioned and configured to detect scattered light from themeasurement chamber; and a processor responsive to the detector andoperative to calculate a zeta potential based on a plurality ofdetection signals from a plurality of different locations relative to asample in the measurement volume.
 2. The apparatus of claim 1 whereinthe processor is operative to calculate the zeta potential based onmovement of tracer particles detected by the detector.
 3. The apparatusof claim 2 wherein the processor is operative to determine tracerparticle movement by Doppler analysis of the scattered light.
 4. Theapparatus of claim 1 wherein the apparatus is responsive to the detectorto perform an autocorellating PALS detection.
 5. The apparatus of claim1 wherein the apparatus is further operative to apply an alternatingvoltage to an opposed pair of electrodes.
 6. The apparatus of claim 5wherein the alternating voltage comprises half cycles of 75 ms or longerin duration.
 7. The apparatus of claim 6 wherein the half cycles arebetween 75 ms and 1200 ms in duration.
 8. The apparatus of claim 1wherein the apparatus is further operative to electrically actuate anactuation mechanism to adjust a sample location relative to the laserbeam.
 9. The apparatus of claim 1 wherein the laser light source isconfigured to provide multiple light beams through the measurementchamber.
 10. The apparatus of claim 1 wherein the detector is configuredto detect scattered light from multiple detection points over the rangeof distances from the sample surface.
 11. The apparatus of claim 1wherein the processor is operative to receive signals from steps ofmanually adjusting an accessory to obtain the plurality of detectionsignals from a plurality of different locations.
 12. The apparatus ofclaim 1 wherein the processor is operative to receive signals from stepsof automatically adjusting an accessory to obtain the plurality ofdetection signals from a plurality of different locations.